We note that for the Ising model on a body-centered-cubic lattice the temperature ${T}_{R}(J)$ of the roughening transition approaches zero when the second-neighbor coupling $J$ vanishes; the interface (100) between regions of opposite magnetization is, at low temperatures, rigid for $J$ positive and becomes rough for $J$ negative. A reinterpretation of van Beijeren's body-centered solid-on-solid model yields a rigorous description of the asymptotic behavior around the limit point $T=0$, $J=0$. In particular, the roughening transition of the solid-on-solid model corresponds to a roughening transition of the isotropic Ising model when crossing a line with critical slope at $T=0$, $J=0$.